Combining two manifold objects creates a non-manifold with issues
Firstly I think you have your terminology backwards. non manifold is bad, manifold is good.
It looks to me that you are trying to attach a bolt head to a cylinder. The problem with using bridge edge loops to do this is that the cylinder has empty space on the inside while the nut does not. this means that you are asking the printer to print faces with 0 thickness, which is impossible so the slicer ignores it or bugs out.
In order to make that a manifold print I would recommend doing 2 things.
Firstly select the bottom face of your bolt and hit I to create an extra perimeter.

now that you have 2 perimeters you can bridge both the inside and outside of the cylinder.
make sure you remember to fill the hole that this creates in the bottom of the nut.

Finally go inside and delete any faces edges or vertices that you would consider to be inside the final 3d printed item.

That should give you a manifold model.